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Folded Cauchy Distribution

This formula can be expressed in terms of the standard formulas for the Cauchy distribution (call the cdf $C\left(x\right)$ and the pdf $d\left(x\right)$ ). if $Y$ is cauchy then $\left|Y\right|$ is folded cauchy. Note that $x\geq0.$

$$\begin{eqnarray*} f\left(x;c\right) & = & \frac{1}{\pi\left(1+\left(x-c\right)^{2}\right)}+\frac{1}{\pi\left(1+\left(x+c\right)^{2}\right)}\\ F\left(x;c\right) & = & \frac{1}{\pi}\tan^{-1}\left(x-c\right)+\frac{1}{\pi}\tan^{-1}\left(x+c\right)\\ G\left(q;c\right) & = & F^{-1}\left(x;c\right)\end{eqnarray*}$$

No moments

Implementation: scipy.stats.foldcauchy